Seems like the pirate environment is especially suited to this type of democracy. Pirate ships operate outside the protections afforded by law, so the only thing really preventing pirate captains from being ousted (or murdered) is the crew's support.

I guess a CEO would need to maintain shareholder support, but shareholders are generally fairly disconnected from the company's day to day operations. Most individuals own shares through mutual funds or ETFs, which means they don't actually have share ownership themselves and can't vote. All you have is the fund owing you a fiduciary duty to vote in your best interests, which generally translates to whatever makes the most money. So the CEO just needs to keep a few large institutions happy, and possibly some large wealthy individual shareholders that he knows from the rotary club (where the heads of aforementioned institutions are also members)

In other words, the way the financial system is set up systematically deprives the less wealthy from their right to have a say in the operation of the companies they nominally own a part of.